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1

Dönges, Philipp, Thomas Götz, Nataliia Kruchinina, et al. "SIR Model for Households." SIAM Journal on Applied Mathematics 84, no. 4 (2024): 1460–81. http://dx.doi.org/10.1137/23m1556861.

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2

Tchuenche, Jean M. "A $$\textit{SIR}$$ SIR epidemic model with incubation period." Afrika Matematika 26, no. 1-2 (2013): 77–85. http://dx.doi.org/10.1007/s13370-013-0189-8.

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3

Marline, Ilha da Silva, Chaves Marques Joice, Otazu Conza Adelaida, De Cezaro Adriano, and Carla Ferreira Nicola Gomes Ana. "The Stiffness Phenomena for the Epidemiological SIR Model: a Numerical Approach." Latin-American Journal of Computing 10, no. 2 (2023): 32–45. https://doi.org/10.5281/zenodo.8067335.

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Mathematical models are among the most successful strategies for predicting the dynamics of a disease spreading in a population. Among them, the so-called compartmental models, where the total population is proportionally divided into compartments, are widely used. The SIR model (Susceptible-Infected-Recovered) is one of them, where the dynamics between the compartments follows a system of nonlinear differential equations. As a result of the non-linearity of the dynamics, it has no analytical solution. Therefore, some numerical methods must be used to obtain an approximate solution. In this co
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4

Johnny, Luís Mércuri, Elis Machiavelli do Carmo Maria, Messias da Silva Almiria, and Tadach Araujo de Oliveira Hammhwygem. "O MODELO COMPARTIMENTAL SIR E UMA APLICAÇÃO PARA OS CASOS DE COVID-19 NA REGIÃO SUDESTE BRASILEIRA." Revistaft 28, no. 133 (2024): 38. https://doi.org/10.5281/zenodo.11103838.

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Neste artigo &eacute; apresentado um estudo sobre o n&uacute;mero de casos de pessoas infectadas pela COVID-19 na regi&atilde;o sudeste brasileira no ano de 2024. Para tal, buscou-se analisar o n&uacute;mero de casos de pessoas infectadas em toda regi&atilde;o sudeste nas nove primeiras semanas epidemiol&oacute;gicas e com base nos resultados obtidos, aplicar o modelo compartimental&nbsp;<em>SIR&nbsp;</em>(suscet&iacute;veis &ndash; infectados &ndash; recuperados) e gerar algumas curvas ao fixar a taxa de recupera&ccedil;&atilde;o e variar a taxa de infec&ccedil;&atilde;o para alguns valores,
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5

Kaddar, Abdelilah, Abdelhadi Abta, and Hamad Talibi Alaoui. "A comparison of delayed SIR and SEIR epidemic models." Nonlinear Analysis: Modelling and Control 16, no. 2 (2011): 181–90. http://dx.doi.org/10.15388/na.16.2.14104.

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In epidemiological research literatures, a latent or incubation period can be medelled by incorporating it as a delay effect (delayed SIR models), or by introducing an exposed class (SEIR models). In this paper we propose a comparison of a delayed SIR model and its corresponding SEIR model in terms of local stability. Also some numerical simulations are given to illustrate the theoretical results.
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6

TAMAI, Seiichiro. "The New Intellectual Property Management Model (SIR Model)." Journal of the Surface Finishing Society of Japan 65, no. 5 (2014): 200–206. http://dx.doi.org/10.4139/sfj.65.200.

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7

Switkes, Jennifer. "A Modified Discrete SIR Model." College Mathematics Journal 34, no. 5 (2003): 399. http://dx.doi.org/10.2307/3595827.

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8

Imane, El Berrai, Bouyaghroumni Jamal, Namir Abdelouahed, and Ezzbady Souad. "Stochastic study for SIR model." Applied Mathematical Sciences 8 (2014): 405–13. http://dx.doi.org/10.12988/ams.2014.311643.

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9

Tornatore, Elisabetta, and Stefania Maria Buccellato. "On a stochastic SIR model." Applicationes Mathematicae 34, no. 4 (2007): 389–400. http://dx.doi.org/10.4064/am34-4-2.

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10

Satsuma, J., R. Willox, A. Ramani, B. Grammaticos, and A. S. Carstea. "Extending the SIR epidemic model." Physica A: Statistical Mechanics and its Applications 336, no. 3-4 (2004): 369–75. http://dx.doi.org/10.1016/j.physa.2003.12.035.

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11

Zhang, Xianghua, and Ke Wang. "Stochastic SIR model with jumps." Applied Mathematics Letters 26, no. 8 (2013): 867–74. http://dx.doi.org/10.1016/j.aml.2013.03.013.

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12

Ritika, Singh, Panchani Nilansh, and Bhatnagar Aastha. "Analysis and Simulation of COVID-19." International Journal of Innovative Technology and Exploring Engineering (IJITEE) 10, no. 7 (2021): 51–54. https://doi.org/10.35940/ijitee.G8928.0510721.

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India is facing a severe second wave of COVID-19 which is much worse than the first wave. It is spreading much faster. India has now surpassed U.S. in terms of daily COVID-19 cases. This paper aims to analyze the trend of COVID 19 and examine why second wave happened and why it is so bad by simulating a simple SEIR model. Which is a compartmental model based on 4 compartments Susceptible, Exposed, Infectious, Recovered.
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13

DISHMEMA, Elfrida, and Lulezim HANELLI. "A SIR Model for Measles Disease Case for Albania." International Journal of Innovative Research in Engineering & Management 6, no. 4 (2019): 38–43. http://dx.doi.org/10.21276/ijirem.2019.6.4.3.

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14

Monaldo, Frank M., and Robert C. Beal. "Comparison of SIR-C SAR wavenumber spectra with WAM model predictions." Journal of Geophysical Research: Oceans 103, no. C9 (1998): 18815–25. http://dx.doi.org/10.1029/98jc01457.

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15

Rohimasanti, Wulan, Respatiwulan Respatiwulan, and Hasih Pratiwi. "MODEL EPIDEMI STOKASTIK SIR RANTAI BINOMIAL." Seminar Nasional Official Statistics 2020, no. 1 (2021): 1239–46. http://dx.doi.org/10.34123/semnasoffstat.v2020i1.674.

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Epidemi adalah kejadian berjangkitnya suatu penyakit menular dalam masyarakat dengan jumlah penderitanya meningkat secara nyata pada waktu dan daerah tertentu. Model Susceptible Infected Recovered (SIR) merupakan suatu model epidemi yang menggambarkan proses penyebaran penyakit dengan karakteristik setiap individu sembuh memiliki kekebalan tubuh permanen. Jumlah individu yang terinfeksi diasumsikan berdistribusi binomial dengan periode penyembuhan bagi individu yang terinfeksi berhingga (ℜ&lt;∞), sehingga individu yang terinfeksi hanya dapat menginfeksi individu lain pada periode ini. Periode
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16

Hebbert, Michael. "Professor Sir Peter Hall: Role Model." Built Environment 41, no. 1 (2015): 5–8. http://dx.doi.org/10.2148/benv.41.1.5.

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17

Imane, El Berrai, Bouyaghroumni Jamal, and Namir Abdelouahed. "Dissemination of epidemic for SIR model." Applied Mathematical Sciences 7 (2013): 6793–800. http://dx.doi.org/10.12988/ams.2013.310594.

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18

CHEN, GUOTING, and TIECHENG LI. "STABILITY OF STOCHASTIC DELAYED SIR MODEL." Stochastics and Dynamics 09, no. 02 (2009): 231–52. http://dx.doi.org/10.1142/s0219493709002658.

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A stochastic version of the SIR model is investigated in this paper. The stability in probability of the steady state of the system is proved under suitable conditions on the white noise perturbations. Linearizations of the systems both with and without delay are given and their exponentially mean square stabilities are studied.
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19

Hällqvist, Robert, Erik Herzog, Johanna Wallén Axehill, and John R. Palmer. "Excuse me Sir/Madam, which Model?" INCOSE International Symposium 34, no. 1 (2024): 1560–78. http://dx.doi.org/10.1002/iis2.13225.

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AbstractDevelopment of complex systems through the application of Model‐Based Systems Engineering (MBSE) will require the creation and maintenance of multiple models, created using multiple languages. Hence, structuring the models such that there is efficient support for incremental development requires some foresight. Having models with multiple or unclear purposes may introduce situations where parts of the organisation will ask for modification for representing a desired future system state, whereas other parts of the organisation require it to remain unchanged in order to represent the pre
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20

Angstmann, C. N., B. I. Henry, and A. V. McGann. "A fractional-order infectivity SIR model." Physica A: Statistical Mechanics and its Applications 452 (June 2016): 86–93. http://dx.doi.org/10.1016/j.physa.2016.02.029.

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21

Montoya, José A., Gudelia Figueroa-Preciado, and Mayra Rosalia Tocto-Erazo. "FLAT LIKELIHOODS: SIR-POISSON MODEL CASE." Revista de la Facultad de Ciencias 11, no. 2 (2022): 74–99. http://dx.doi.org/10.15446/rev.fac.cienc.v11n2.100986.

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Systems of differential equations are used as the basis to define mathematical structures for moments, like the mean and variance, of random variables probability distributions. Nevertheless, the integration of a deterministic model and a probabilistic one, with the aim of describing a random phenomenon, and take advantage of the observed data for making inferences on certain population dynamic characteristics, can lead to parameter identifiability problems. Furthermore, approaches to deal with those problems are usually inappropriate. In this paper, the shape of the likelihood function of a S
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22

Scrucca, Luca. "Model-based SIR for dimension reduction." Computational Statistics & Data Analysis 55, no. 11 (2011): 3010–26. http://dx.doi.org/10.1016/j.csda.2011.05.006.

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23

Pakes, Anthony G. "A SIR Epidemic Model Allowing Recovery." Axioms 13, no. 2 (2024): 115. http://dx.doi.org/10.3390/axioms13020115.

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The deterministic SIR model for disease spread in a closed population is extended to allow infected individuals to recover to the susceptible state. This extension preserves the second constant of motion, i.e., a functional relationship of susceptible and removed numbers, S(t) and R(t), respectively. This feature allows a substantially complete elucidation of qualitative properties. The model exhibits three modes of behaviour classified in terms of the sign of −S′(0), the initial value of the epidemic curve. Model behaviour is similar to that of the SIS model if S′(0)&gt;0 and to the SIR model
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24

Ali Shah, Syed Tahir, Majad Mansoor, Adeel Feroz Mirza, et al. "Predicting COVID-19 Spread in Pakistan using the SIR Model." Journal of Pure and Applied Microbiology 14, no. 2 (2020): 1423–30. http://dx.doi.org/10.22207/jpam.14.2.40.

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25

Rohmah, Awawin Mustana, Siti Alfiatur Rohmaniah, and Rifky Ardhana Kisno Saputra. "Model Kontrol Optimal SIR Pada Penyakit Campak." Unisda Journal of Mathematics and Computer Science (UJMC) 8, no. 1 (2022): 67–74. http://dx.doi.org/10.52166/ujmc.v8i1.3226.

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The SIR model is one of the epidemic models to describe the spread of infectious diseases with healing and without immunity to these infections. Environmental changes can affect changes in disease patterns that can cause endemic. One of the diseases that cause endemic is Measles (Measles). Therefore, it is necessary to take preventive measures to reduce the rate of spread of the disease, the most effective measure to prevent the spread of the disease is vaccination. Measles transmission prevention events that occur in a population can be modeled in a mathematical form, one of which is the SIR
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26

Pasaribu, Donna Mesina Rosadini, Ernawaty Tamba, Muhammad Faturrahman Adani, and Wani Devita Gunardi. "Literature Review: Model Matematika Penyebaran Virus SARS-COV-2 pada Masa Pandemi COVID-19 Tahun 2020." Jurnal Kedokteran Meditek 29, no. 2 (2023): 226–35. http://dx.doi.org/10.36452/jkdoktmeditek.v29i2.2607.

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Pandemi COVID-19 dinyatakan sebagai Public Health Emergency of International Concern oleh WHO. Model Matematika penyebaran Susceptible-Infected-Recovered (SIR) dan model Susceptible-Exposed-Infected-Recovered (SEIR) digunakan dalam pemodelan penyakit menular dengan menghitung jumlah orang dalam populasi tertutup. Pemodelan matematika ini merupakan matematika epidemiologi untuk memahami dinamika populasi pada saat pandemi, dan acuan efektivitas kebijakan yang dilakukan selama pandemi. Literatur Riview ini bertujuan untuk mengetahui gambaran situasi pandemi COVID-19 berdasarkan model matematika
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27

Rizki Andrian Fitra, Muhammad, Sybil Auzi, Neysa Talitha Jehian, and Debi Yandra Niska. "PENGEMBANGAN MODEL SIMULASI PENYEBARAN WABAH PENYAKIT MENULAR MENGGUNAKAN METODE SEIR DAN SIR." JATI (Jurnal Mahasiswa Teknik Informatika) 9, no. 4 (2025): 6201–6. https://doi.org/10.36040/jati.v9i4.14014.

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Penyebaran wabah penyakit menular seperti COVID-19 dan kolera menjadi tantangan global yang memerlukan pendekatan ilmiah berbasis simulasi untuk mitigasi yang efektif. Namun, masih terbatasnya model simulasi yang mampu menggabungkan pendekatan matematis dan visualisasi interaktif secara fleksibel menjadi tantangan dalam memahami dinamika penyebaran wabah secara lebih komprehensif. Penelitian ini bertujuan untuk mengembangkan simulasi berbasis model SIR dan SEIR yang lebih akurat dan mudah dianalisis untuk mendukung perencanaan strategi mitigasi. Simulasi dilakukan dengan parameter populasi awa
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28

Bougoffa, Lazhar, Smail Bougouffa, and Ammar Khanfer. "Approximate and Parametric Solutions to SIR Epidemic Model." Axioms 13, no. 3 (2024): 201. http://dx.doi.org/10.3390/axioms13030201.

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This article provides a detailed exploration of the SIR epidemic model, starting with its meticulous formulation. The study employs a novel approach called the upper and lower bounds technique to approximate the solution to the SIR model, providing insights into the dynamic interplay between susceptible S, infected I, and recovered R populations. A new parametric solution to this model has been presented. Applying the Adomian decomposition method (ADM) allows for the attaining of highly accurate approximate solutions in the context of the SIR epidemic model. To validate the accuracy and robust
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29

Wang, Yan, Guichen Lu, and Jiang Du. "Calibration and prediction for the inexact SIR model." Mathematical Biosciences and Engineering 19, no. 3 (2022): 2800–2818. http://dx.doi.org/10.3934/mbe.2022128.

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&lt;abstract&gt;&lt;p&gt;A Susceptible Infective Recovered (SIR) model is usually unable to mimic the actual epidemiological system exactly. The reasons for this inaccuracy include observation errors and model discrepancies due to assumptions and simplifications made by the SIR model. Hence, this work proposes calibration and prediction methods for the SIR model with a one-time reported number of infected cases. Given that the observation errors of the reported data are assumed to be heteroscedastic, we propose two predictors to predict the actual epidemiological system by modeling the model d
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30

Pathak, S., A. Maiti, and G. P. Samanta. "Rich dynamics of an SIR epidemic model." Nonlinear Analysis: Modelling and Control 15, no. 1 (2010): 71–81. http://dx.doi.org/10.15388/na.2010.15.1.14365.

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This paper aims to study an SIR epidemic model with an asymptotically homogeneous transmission function. The stability of the disease-free and the endemic equilibrium is addressed. Numerical simulations are carried out. Implications of our analytical and numerical findings are discussed critically.
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31

Vinitsky, S. I., A. A. Gusev, V. L. Derbov, P. M. Krassovitskiy, F. M. Pen’kov, and G. Chuluunbaatar. "Reduced SIR Model of COVID-19 Pandemic." Computational Mathematics and Mathematical Physics 61, no. 3 (2021): 376–87. http://dx.doi.org/10.1134/s0965542521030155.

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32

Abueldahab, Sheima M. E., and Franck Kalala Mutombo. "SIR Model and HIV/AIDS in Khartoum." OALib 08, no. 04 (2021): 1–10. http://dx.doi.org/10.4236/oalib.1107334.

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33

Abdulkarim, Umar M. "Stochastic SIR Household Epidemic Model with Misclassification." Open Journal of Statistics 11, no. 05 (2021): 886–905. http://dx.doi.org/10.4236/ojs.2021.115052.

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34

Obolonkin, Vladimir, and Anatoly Zherelo. "Stochastic Generalization of the Epidemiological SIR Model." Nonlinear Phenomena in Complex Systems 24, no. 4 (2021): 409–14. http://dx.doi.org/10.33581/1561-4085-2021-24-4-409-414.

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In this paper we propose stochastic modification of well-known in epidemiology SIR model. This modification allows us to simulate various scenarios of infection and can be used for the risk management.
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35

Bayraktar, Erhan, Asaf Cohen, and April Nellis. "A Macroeconomic SIR Model for COVID-19." Mathematics 9, no. 16 (2021): 1901. http://dx.doi.org/10.3390/math9161901.

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The COVID-19 pandemic and subsequent lockdowns highlight the close and delicate relationship between a country’s public health and economic health. Models that combine macroeconomic factors with traditional epidemic dynamics to calculate the impacts of a disease outbreak are therefore extremely useful for policymakers seeking to evaluate the best course of action in such a crisis. We developed a macroeconomic SIR model that considers herd immunity, behavior-dependent transmission rates, remote workers, and the indirect externalities of lockdowns. It is formulated as an exit time control proble
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36

Elliott, Sean, and Christian Gouriéroux. "Estimated reproduction ratios in the SIR model." Canadian Journal of Statistics 49, no. 4 (2021): 992–1017. http://dx.doi.org/10.1002/cjs.11663.

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37

Hynd, Ryan, Dennis Ikpe, and Terrance Pendleton. "Two critical times for the SIR model." Journal of Mathematical Analysis and Applications 505, no. 2 (2022): 125507. http://dx.doi.org/10.1016/j.jmaa.2021.125507.

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38

Nakamura, Gilberto, Basil Grammaticos, and Mathilde Badoual. "Confinement Strategies in a Simple SIR Model." Regular and Chaotic Dynamics 25, no. 6 (2020): 509–21. http://dx.doi.org/10.1134/s1560354720060015.

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39

El Maroufy, Hamid, Lahcen Omari, and Ziad Taib. "Transition Probabilities for Generalized SIR Epidemic Model." Stochastic Models 28, no. 1 (2012): 15–28. http://dx.doi.org/10.1080/15326349.2011.614201.

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40

ZHANG, TAILEI, JUNLI LIU, and ZHIDONG TENG. "DIFFERENTIAL SUSCEPTIBILITY TIME-DEPENDENT SIR EPIDEMIC MODEL." International Journal of Biomathematics 01, no. 01 (2008): 45–64. http://dx.doi.org/10.1142/s1793524508000059.

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A non-autonomous epidemic dynamical system, in which we include variable susceptibility, is proposed. Some threshold conditions are derived which determine whether or not the disease will go to extinction. Some new threshold values, [Formula: see text], [Formula: see text] and [Formula: see text], are deduced for this general time-dependent system such that when [Formula: see text] is greater than 0, the disease is endemic in the sense of permanence and when one of the threshold values [Formula: see text] and [Formula: see text] is less than 0, the disease will die out. As an application of th
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41

El Maroufy, Hamid, Driss Kiouach, and Taib Ziad. "Final outcome probabilities for SIR epidemic model." Communications in Statistics - Theory and Methods 45, no. 8 (2016): 2426–37. http://dx.doi.org/10.1080/03610926.2014.881494.

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42

Kiouach, D. "Diffusion Approximation of Stochastic SIR Epidemic Model." British Journal of Mathematics & Computer Science 6, no. 3 (2015): 165–71. http://dx.doi.org/10.9734/bjmcs/2015/14808.

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43

Okyere, Eric, Francis Oduro, Samuel Amponsah, Isaac Dontwi, and Nana Frempong. "Fractional Order SIR Model with Constant Population." British Journal of Mathematics & Computer Science 14, no. 2 (2016): 1–12. http://dx.doi.org/10.9734/bjmcs/2016/23017.

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44

WU, JIANJUN, ZIYOU GAO, and HUIJUN SUN. "SIMULATION OF TRAFFIC CONGESTION WITH SIR MODEL." Modern Physics Letters B 18, no. 30 (2004): 1537–42. http://dx.doi.org/10.1142/s0217984904008031.

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The spread of traffic congestion is related to the rate of infection and the recovery rate. In this paper, we describe the traffic congestion spread with SIR model of a complex network. From the point of the complex network, the spread of the traffic congestion with different parameters are simulated. By simulation, we find that the behavior of the traffic system is tightly related to the average rate of infection, the average recovery rate and the topological properties of traffic network.
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45

Saif, M. Ali, M. A. Shukri, and F. H. Al-makhedhi. "Dynamics of SIR Model on Random Networks." مجلة جامعة عمران 4, no. 7 (2024): 10. http://dx.doi.org/10.59145/jaust.v4i7.91.

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we focus on studying the dynamics of infectious disease spreading SIR model on random networks. We investigate how various parameters of the network influence the behavior of spreading and analyze the occurrence of phase transitions within this networkframework. Our analysis reveals the critical role of network connectivity in shaping the dynamics of disease transmission and highlights the presence of mean-field phase transitions.Additionally, we employ both analytical techniques and simulation methods to extract critical thresholds for the model and compare them for validation. By delving int
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46

Kumar, Roshan, and Smita Dey. "SIR Model for Ebola Outbreak in Liberia." International Journal of Mathematics Trends and Technology 28, no. 1 (2015): 28–30. http://dx.doi.org/10.14445/22315373/ijmtt-v28p506.

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47

Husain, H. S. "An SIR mathematical model for Dipterid disease." Journal of Physics: Conference Series 1280 (November 2019): 022051. http://dx.doi.org/10.1088/1742-6596/1280/2/022051.

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48

Kuin, Roger. "Sir Philip Sidney's Model of the Statesman." Reformation 4, no. 1 (1999): 93–117. http://dx.doi.org/10.1179/ref_1999_4_1_006.

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49

Kim, Kwang Ik, Zhigui Lin, and Qunying Zhang. "An SIR epidemic model with free boundary." Nonlinear Analysis: Real World Applications 14, no. 5 (2013): 1992–2001. http://dx.doi.org/10.1016/j.nonrwa.2013.02.003.

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50

Mullan, Peter, and Thomas Gluck. "Sir John Soane's House and Museum model." Architectural Research Quarterly 2, no. 4 (1997): 12–21. http://dx.doi.org/10.1017/s135913550000155x.

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This paper describes a model of Sir John Soane's House and Museum which was executed as an independent study during the authors' Third Year at Yale University School of Architecture. Having visited the building independently of each other and having returned with a similar mystified curiosity, they initiated the project as an attempt to further understand the house by developing an analytical method of representation specific to it. The model was constructed from drawings prepared by the authors which synthesised information from available published documentation and drawings obtained from the
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